Two-dimensional Analogue Research Articles

Topological defects in smectic islands formed in antiferroelectric freestanding nanofilms

In this work, the authors studied the orientational structure of islands formed in freestanding films as disc-like regions whose number of smectic layers is greater than that in the film. Islands were prepared in thin smectic nanofilms in which the long molecular axes tilt with respect to the normal layer. Geometric restrictions and rigid boundary conditions for the molecular orientation on the boundary of the island and the film induce frustration in the field of molecular ordering and lead to formation of topological defects. Depolarized reflected light microscopy allows the determination of the type of topological defects. Defects with topological charges S = +2, +1, −1, −1/2 were located inside the islands and on their boundary with the film. In the islands, the authors observed unusual structures formed by a complex of defects with positive and negative topological charges. The orientational structure of the field of molecular ordering was calculated taking into account the real and virtual topological defects on the island boundary. Islands with topological defects can be considered as a two-dimensional analogue of a mesoscopic atom.

In-plane band bending in hexagonal monolayer WS2 by edge polarization

A triangular domain structure within hexagonal monolayer ${\mathrm{WS}}_{2}$ is found to be induced by edge polarization. Based on density-functional theory calculations, the local electrostatic potential over ${\mathrm{WS}}_{2}$ is investigated, and with the S-adatom and ${\mathrm{S}}_{2}$-addimer reconstructions at the W edges, the domains facing the W edges are found to be lower by up to 1.8 eV in the electrostatic potential than those facing the S edges. The edge-induced band bending in the terminated two-dimensional system is a two-dimensional analogy of the surface band bending effect in the terminated three-dimensional system. The largest potential difference is found to be comparable to the electronic gap of ${\mathrm{WS}}_{2}$, and near the edges, the W and S domains can be $n$- and $p$-type doped, respectively, by which the hexagonal monolayer ${\mathrm{WS}}_{2}$ can be applied to a bipolar electronic junction device.

Direct-Bandgap 2D Silver-Bismuth Iodide Double Perovskite: The Structure-Directing Influence of an Oligothiophene Spacer Cation.

Three-dimensional (3D) hybrid organic-inorganic lead halide perovskites (HOIPs) feature remarkable optoelectronic properties for solar energy conversion but suffer from long-standing issues of environmental stability and lead toxicity. Associated two-dimensional (2D) analogues are garnering increasing interest due to superior chemical stability, structural diversity, and broader property tunability. Toward lead-free 2D HOIPs, double perovskites (DPs) with mixed-valent dual metals are attractive. Translation of mixed-metal DPs to iodides, with their prospectively lower bandgaps, represents an important target for semiconducting halide perovskites, but has so far proven inaccessible using traditional spacer cations due to either intrinsic instability or formation of competing non-perovskite phases. Here, we demonstrate the first example of a 2D Ag-Bi iodide DP with a direct bandgap of 2.00(2) eV, templated by a layer of bifunctionalized oligothiophene cations, i.e., (bis-aminoethyl)bithiophene, through a collective influence of aromatic interactions, hydrogen bonding, bidentate tethering, and structural rigidity. Hybrid density functional theory calculations for the new material reveal a direct bandgap, consistent with the experimental value, and relatively flat band edges derived principally from Ag-d/I-p (valence band) and Bi-p/I-p (conduction band) states. This work opens up new avenues for exploring specifically designed organic cations to stabilize otherwise inaccessible 2D HOIPs with potential applications for optoelectronics.

Surface acoustic waves over bianisotropic metasurfaces

Metasurfaces are the two-dimensional planarized analogues of metamaterials, yielding unique sound manipulation along a surface. Our group recently proposed the concept of bianisotropic metasurfaces achieved by exploiting the strong nonlocal coupling between neighboring vibrating units, yielding anisotropic impedance in airborne acoustics, and we have applied this property to realize acoustic hyperbolic metasurfaces, which require extreme impedance anisotropy. In this talk, we investigate the wave propagation properties of bianisotropic metasurfaces and report all-angle backward-wave propagation on the surface. By carefully designing the coupling between unit cells, both negative phase index and energy index for surface acoustic waves are observed above the metasurface for all propagation directions, hence realizing converging waves for a radiating point source. Since in bianisotropic metasurfaces the energy can be transmitted not only through surface waves, but also through the coupling units, negative energy index for surface waves does not violate energy conservation laws, as it can be sustained by a positive energy flow within the connected unit cells composing the metasurface.

Proposal for an analog Schwarzschild black hole in condensates of light

By etching a hole in the mirrors or by placing a scatterer in the center of a cavity, we can create a sink for light. In a Bose-Einstein condensate of photons this sink results in the creation of a so-called radial vortex, which is a two-dimensional analogue of a Schwarzschild black hole. We theoretically investigate the Hawking radiation and the associated greybody factor of this Schwarzschild black hole. In particular, we determine the density-density and velocity-velocity correlation functions of the Hawking radiation, which can be measured by observing the spatial correlations in the fluctuations in the light emitted by the cavity.

Application of a directional palladium-103 brachytherapy device on a curved surface.

The directional planar palladium-103 LDR device (CivaSheet ) may be used for intraoperative implantation at the interface between the tumor site and healthy tissue. Its dosimetric properties have been studied in the ideal case of application on a flat surface. The dosimetric impact of implanting this highly directional device on a curved surface that may be encountered in clinical treatments is analyzed. CivaSheet is designed as an array of directional palladium-103 sources (CivaDots). From the postoperative computed tomography (CT) scans of three patients, the shape of each implanted CivaSheet was reconstructed. In order to obtain a realistic estimate of the distribution of curvatures, the mean radius of curvature at the location of each CivaDot was calculated. A Monte Carlo simulation (FLUKA) of a single CivaDot was designed, based upon published geometry and material specifications. Both the radial dose function analog and the two-dimensional anisotropy function analog for the CivaDot were validated in comparison with film measurements and benchmarked to published Monte Carlo data. A value for the dose-rate constant Λ=0.587(19)cGy/h/U for a CivaDot source in water was calculated as well. Knowledge of the dose distribution in the vicinity of each source allowed the dose at any point around CivaSheets of different curvatures and orientations to be calculated. The local radius of curvature was found to be primarily between 2 and 8cm in all three patient implants. On the unshielded side of an inward-facing curved CivaSheet implant of radius 2cm, the calculated dose at 0.5cm depth exceeded the prescribed dose by ∼20%, while on the shielded side the dose increased by a factor of two, thus compromising the shielding efficiency of the original design. On the unshielded side of an outward-facing curved implant, the dose at 0.5cm depth decreased by ∼20%. When tumor bed curvature can be estimated from the preplanning CT scan, the results from this study provide quantitative guide for modifying the source strength to achieve the desired clinical results. In many intraoperative cases, however, accurate preplanning based on surface curvature may not be practical. In such situations, knowledge of the dosimetric impact of the surface curvature provides motivation for avoiding implantation geometries that can lead to either over/underdosing the target, or excess dose to healthy tissue.

Edge states in a two-dimensional nonsymmorphic semimetal

Dirac materials have unique transport properties, partly due to the presence of surface states. A new type of Dirac materials, protected by non-symmorphic symmetries was recently proposed by Young and Kane [1]. By breaking of time reversal or inversion symmetry one can split the Dirac cones into Weyl nodes. The later are characterized by local Chern numbers, that makes them two-dimensional analogs of Weyl semimetals. We find that the formation of the Weyl nodes is accompanied by an emergence of one-dimensional surface states, similar to Fermi arcs in Weyl semimetals and edge states in two-dimensional graphene. We explore these states for a quasi-one-dimensional non-symmorphic ribbon. The type and strength of applied deformation control the location and Weyl nodes and their composition. This determines the properties of emerging edge states. The sensitivity of these edge states to the external deformations makes non-symmorphic materials potentially useful as a new type of electromechanical sensors.

Numerical simulation of the Saffman-Taylor instability in the Hele-Show cell

The process of displacing one viscous liquid with a less viscous one in porous medium is accompanied by folds formation on the border of liquids division. These folds called ‘viscous fingers’ grow with not the same velocity. This phenomenon doesn’t allow extracting all oil while displacing it with water. The process of formation and growth of viscous fingers has a critical sustainability which depends on a number of parameters. One of these parameters is characteristics of imposed oscillations. Practical field experiments demonstrate the impact that imposed oscillations have on the watercut of extracted oil. Two-dimensional analogue of displacing oil with water is displacing viscous liquid from Hele-Show cell. The impact of characteristics of initial oscillation on the ‘viscous fingers’ formation and development process is studied in this paper. Dependencies of relative growth velocities of ‘viscous fingers’ on amplitude and frequency of influence are presented below.

Uniqueness of Banach space valued graphons

A Banach space valued graphon is a function W : ( Ω , A , π ) 2 → Z from a probability space to a Banach space with a separable predual, measurable in a suitable sense, and lying in appropriate L p -spaces. As such we may consider W ( x , y ) as a two-variable random element of the Banach space. A two-dimensional analogue of moments can be defined with the help of graphs and weak-* evaluations, and a natural question that then arises is whether these generalized moments determine the function W uniquely – up to measure preserving transformations. The main motivation comes from the theory of multigraph limits, where these graphons arise as the natural limit objects for convergence in a generalized homomorphism sense. Our main result is that this holds true under some Carleman-type condition, but fails in general even with Z = R , for reasons related to the classical moment-problem. In particular, limits of multigraph sequences are uniquely determined – up to measure preserving transformations – whenever the tails of the edge-distributions stay small enough.

Two-dimensional graphdiyne analogue Co-coordinated porphyrin covalent organic framework nanosheets as a stable electrocatalyst for the oxygen evolution reaction

Employing metalloporphyrin as monomer is an effective strategy to overcome the drawback of graphdiyne in electrocatalytic process. The Co–N4 active centers, expanded pores, and conjugated structure altogether endow the Co-PDY with excellent OER catalytic performance.

Bifunctional Organic Spacers for Formamidinium-Based Hybrid Dion-Jacobson Two-Dimensional Perovskite Solar Cells.

Three-dimensional (3D) perovskite materials display remarkable potential in photovoltaics owing to their superior solar-to-electric power conversion efficiency, with current efforts focused on improving stability. Two-dimensional (2D) perovskite analogues feature greater stability toward environmental factors, such as moisture, owing to a hydrophobic organic cation that acts as a spacer between the inorganic layers, which offers a significant advantage over their comparatively less stable 3D analogues. Here, we demonstrate the first example of a formamidinium (FA) containing Dion-Jacobson 2D perovskite material characterized by the BFA n-1Pb nI3 n+1 formulation through employing a novel bifunctional organic spacer (B), namely 1,4-phenylenedimethanammonium (PDMA). We achieve remarkable efficiencies exceeding 7% for (PDMA)FA2Pb3I10 based 2D perovskite solar cells resisting degradation when exposed to humid ambient air, which opens up new avenues in the design of stable perovskite materials.

Elastic Waves in Curved Space: Mimicking a Wormhole.

Transformation optics (TO) can be used to investigate nontrivial spacetime structures with inhomogeneous materials. However, the extreme curvature and large refractive indices make the implementation of a wormhole challenging. By considering flexural waves on a curved plate with geometric curvature, the stringent material requirement can be relaxed, and we demonstrate a two-dimensional analog of a wormhole using homogeneous materials within a curved laboratory frame. TO is used to understand wave propagation in such a curved space. This curved elastic space approach allows us to investigate not only geodesics but also wave redirection, tunneling, and virtual caustics of the wormhole, and will be useful to develop curvature-driven wave front shaping in general.

Virial coefficients of one-dimensional and two-dimensional Fermi gases by stochastic methods and a semiclassical lattice approximation

We map out the interaction effects on the first six virial coefficients of one-dimensional Fermi gases with zero-range attractive and repulsive interactions, and the first four virial coefficients of the two-dimensional analog with attractive interactions. To that end, we use two non-perturbative stochastic methods: projection by complex stochastic quantization, which allows us to determine high-order coefficients at weak coupling and estimate the radius of convergence of the virial expansion; and a path-integral representation of the virial coefficients. To complement our numerical calculations, we present leading-order results in a semiclassical lattice approximation, which we find to be surprisingly close to the expected answers.

Surface Engineering of Chemically Exfoliated MoS2 in a “Click”: How To Generate Versatile Multifunctional Transition Metal Dichalcogenides-Based Platforms

The interest for transition metal dichalcogenides (TMDs) as two-dimensional (2D) analogues of graphene is steadily growing along with the need of efficient and easy tunable protocols for their surface functionalization. This latter aspect holds a key role in the widespread application of TMDs in various technological fields and it represents the missing step to bridge the gap between the more popular C sp2-based networks and their inorganic counterparts. Although significant steps forward have already been made in the field of TMDs functionalization (particularly for MoS2), a rational approach to their surface engineering for the generation of 2D organic–inorganic hybrids capable to accommodate various molecules featured by orthogonal groups has not been reported yet. The paper paves the way toward a new frontier for “click” chemistry in material science. It describes the post-synthetic modification (PSM) of covalently decorated MoS2 nanosheets with phenylazido pendant arms and the successful application of CuAAC chemistry (copper-mediated azide–alkyne cycloaddition) towards the generation of highly homo- and hetero-decorated MoS2 platforms. This contribution goes beyond the proof of evidence of the chemical grafting of organic groups to the surface of exfoliated MoS2 flakes through covalent C–S bonds. It also demonstrates the versatility of the hybrid samples to undergo post-synthetic modifications thus imparting multimodality to these 2D materials. Several physico-chemical [SEM microscopy, fluorescence lifetime imaging (FLIM)], spectroscopic (IR, Raman, XPS, UV–vis), and analytical tools have been combined together for the hybrids’ characterization as well as for the estimation of their functionalization loading.

Two-Dimensional Drexhage Experiment for Electric- and Magnetic-Dipole Sources on Plasmonic Interfaces.

Fifty years ago, Drexhage et al. showed how photon emission from an electric dipole can be modified by a nearby mirror. Here, we study the two-dimensional analog for surface plasmon polaritons (SPPs). We print Eu^{3+}-doped nanoparticles, which act as both electric- and magnetic-dipole sources of SPPs, near plasmonic reflectors on flat Ag films. We measure modified SPP radiation patterns and emission rates as a function of reflector distance and source symmetry. The results, which agree with an analytical self-interference model, provide simple strategies to control SPP radiation in plasmonic devices.

Description of the Adsorption Equilibrium with Consideration to the Decreasing Availability of Space in the Course of Mobile Adsorption of a Single Gas on a Homogenous Surface of Solid

Abstract The subsequent stages of the process of formulation of the equation for gas adsorption on a homogenous surface of a solid adsorbent were presented based on the general expression for the canonical ensemble of the mobile single-component adsorption monolayer. The method of formulating the configuration integral of the proposed model was discussed in detail where the role both of the attraction and repulsion between adsorbed molecules was emphasised. The expression for the probability of finding a molecule in a specified point on a surface of an adsorbent was modified by determining its magnitude by the adsorbent concentration. The expression for the so-called effective surface of the adsorbent was obtained by adapting a two-dimensional analogue equation of state hard spheres – Van der Waals equation (2D-vdW) and Reis-Frisch-Lebowitz equation accordingly (2D-RFL). As a result, two new adsorption equations were formulated which differ in detail concerning the adsorbate-adsorbate repulsion. On each of these equations theoretical analysis was performed in terms of two-dimensional phase transformation. In both cases it was proved that the proposed solution allows for the presence of two-phase transformations of the first type which is the gas-liquid condensation and solidification liquid-solid. The verification of the given approach was supplemented by the description of the experimental data given in reference literature and by obtaining a very good correlation between the theory and experiment.

Quasi-Two-Dimensional Luminescent Silicon Nanosheets

Although predicted to be stable under ambient conditions, the experimental synthesis of silicene—the two-dimensional silicon analogue of graphene—has been a great challenge. Here, we report the preparation of scalable quantities of crystalline nanosheets of two-dimensional silicon by simple topochemical exfoliation of layered Zintl phases. The simple process leads to the formation of stacked layers of 2D Si nanosheets which are arbitrarily surface terminated with oxygen, hydrogen, hydroxide, and other ligands. The nanosheets exhibit strong room-temperature photoluminescence, and their overall spectroscopic characteristics closely resemble other forms of silicon nanocrystals. Remarkably, the pelletized nanosheets exhibit significantly high Hall mobility even in the absence of any doping or surface treatment, which is better than the reported values of doped Si nanosystems. Such ensembles of two-dimensional nanosheets of silicon bear the signature of exotic electronic properties and represent important building blocks in two-dimensional electronics along with potential applications in solar cells, next-generation thermoelectric materials, and sensors.

Computer modeling and analytical description of structural defects in two-dimensional crystals of bounded sizes: Free boundary, dislocations, and crowdions

Two-dimensional crystals of bounded sizes formed by atoms with centrallysymmetric interaction between them (Lennard-Jones potential) are examined. Methodologies of molecular dynamics have established the atomic structure of clusters of approximately circular form with radii on the nanometer scale. Deviations of atomic configurations from the ideal lattice of a 2D crystal, caused both by the free boundary of a cluster and by the defects introduced into its center, dislocations and crowdions, are investigated. The values of the self-energy of these defects are calculated, and their dependencies on the cluster radius and the parameters of the potential of interatomic interaction are analyzed. Methodologies of continuum mechanics of crystals described the features of uniform elastic strain of 2D crystal circles and bands in comparison with deformation of 3D crystal spheres and rods. Two-dimensional analogues of the main characteristics of elasticity, namely the coefficient of compression, Young's modulus, shear modulus, and Poisson coefficient, as well as their connection with Lamé coefficients, are discussed. The dependencies of the enumerated parameters of elasticity on the parameters of the potential of interatomic interaction are established, and estimates for the effective sizes of kernels of dislocation and crowdion are derived.

A review of gap-surface plasmon metasurfaces: fundamentals and applications

AbstractPlasmonic metasurfaces, which can be considered as the two-dimensional analog of metal-based metamaterials, have attracted progressively increasing attention in recent years because of the ease of fabrication and unprecedented control over the reflected or transmitted light while featuring relatively low losses even at optical wavelengths. Among all the different design approaches, gap-surface plasmon metasurfaces – a specific branch of plasmonic metasurfaces – which consist of a subwavelength thin dielectric spacer sandwiched between an optically thick metal film and arrays of metal subwavelength elements arranged in a strictly or quasi-periodic fashion, have gained awareness from researchers working at practically any frequency regime as its realization only requires a single lithographic step, yet with the possibility to fully control the amplitude, phase, and polarization of the reflected light. In this paper, we review the fundamentals, recent developments, and opportunities of gap-surface plasmon metasurfaces. Starting with introducing the concept of gap-surface plasmon metasurfaces, we present three typical gap-surface plasmon resonators, introduce generalized Snell’s law, and explain the concept of Pancharatnam-Berry phase. We then overview the main applications of gap-surface plasmon metasurfaces, including beam-steerers, flat lenses, holograms, absorbers, color printing, polarization control, surface wave couplers, and dynamically reconfigurable metasurfaces. The review is ended with a short summary and outlook on possible future developments.

On pinned fields, interlacements, and random walk on $$({\mathbb {Z}}/N {\mathbb {Z}})^2$$ ( Z / N Z ) 2

We define two families of Poissonian soups of bidirectional trajectories on $${\mathbb {Z}}^2$$ , which can be seen to adequately describe the local picture of the trace left by a random walk on the two-dimensional torus $$({\mathbb {Z}}/N {\mathbb {Z}})^2$$ , started from the uniform distribution, run up to a time of order $$(N\log N)^2$$ and forced to avoid a fixed point. The local limit of the latter was recently established in Comets et al. (Commun Math Phys 343:129–164, 2016). Our construction proceeds by considering, somewhat in the spirit of statistical mechanics, a sequence of “finite volume” approximations, consisting of random walks avoiding the origin and killed at spatial scale N, either using Dirichlet boundary conditions, or by means of a suitably adjusted mass. By tuning the intensity u of such walks with N, the occupation field can be seen to have a nontrivial limit, corresponding to that of the actual random walk. Our construction thus yields a two-dimensional analogue of the random interlacements model introduced in Sznitman (Ann Math 171(3):2039–2087, 2010) in the transient case. It also links it to the pinned free field in $${\mathbb {Z}}^2$$ , by means of a (pinned) Ray–Knight type isomorphism theorem.